ISA 444: Business Forecasting

.title[
# ISA 444: Business Forecasting
]
.subtitle[
## 01: Introduction to Time Series Analysis and Forecasting
]
.author[
### <br>Fadel M. Megahed, PhD <br><br>Raymond E. Gloss Professor in Business <br> Farmer School of Business<br> Miami University<br><br> <a href="https://www.linkedin.com/in/fadel-megahed-289046b4"><svg viewBox="0 0 448 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M416 32H31.9C14.3 32 0 46.5 0 64.3v383.4C0 465.5 14.3 480 31.9 480H416c17.6 0 32-14.5 32-32.3V64.3c0-17.8-14.4-32.3-32-32.3zM135.4 416H69V202.2h66.5V416zm-33.2-243c-21.3 0-38.5-17.3-38.5-38.5S80.9 96 102.2 96c21.2 0 38.5 17.3 38.5 38.5 0 21.3-17.2 38.5-38.5 38.5zm282.1 243h-66.4V312c0-24.8-.5-56.7-34.5-56.7-34.6 0-39.9 27-39.9 54.9V416h-66.4V202.2h63.7v29.2h.9c8.9-16.8 30.6-34.5 62.9-34.5 67.2 0 79.7 44.3 79.7 101.9V416z" /></svg> <span class="citation">@Fadel</span> Megahed</a> <br> <a href="https://github.com/fmegahed/"><svg viewBox="0 0 496 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z" /></svg> fmegahed</a> <br> <a href="mailto:fmegahed@miamioh.edu"><svg viewBox="0 0 512 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z" /></svg> fmegahed@miamioh.edu</a><br> <a href="https://calendly.com/fmegahed"><svg viewBox="0 0 384 512" style="height:1em;position:relative;display:inline-block;top:.1em;fill:white;" xmlns="http://www.w3.org/2000/svg"> <path d="M202.021 0C122.202 0 70.503 32.703 29.914 91.026c-7.363 10.58-5.093 25.086 5.178 32.874l43.138 32.709c10.373 7.865 25.132 6.026 33.253-4.148 25.049-31.381 43.63-49.449 82.757-49.449 30.764 0 68.816 19.799 68.816 49.631 0 22.552-18.617 34.134-48.993 51.164-35.423 19.86-82.299 44.576-82.299 106.405V320c0 13.255 10.745 24 24 24h72.471c13.255 0 24-10.745 24-24v-5.773c0-42.86 125.268-44.645 125.268-160.627C377.504 66.256 286.902 0 202.021 0zM192 373.459c-38.196 0-69.271 31.075-69.271 69.271 0 38.195 31.075 69.27 69.271 69.27s69.271-31.075 69.271-69.271-31.075-69.27-69.271-69.27z" /></svg> Automated Scheduler for Office Hours</a><br><br>
]
.date[
### Spring 2026
]

---

# Learning Objectives for Today's Class

.font90[
- **Explain why forecasting is both valuable and difficult**, using real-world business and policy examples.

- **Recognize the fundamental limits of forecasting**, including uncertainty, randomness, and the difference between prediction and explanation.

- **Distinguish forecasting problems from other analytics tasks**, such as regression and classification, and explain why time ordering matters.

- **Identify what types of phenomena are forecastable and which are not**, based on the presence or absence of systematic structure.

- **Describe the core components of a time series**, including trend, seasonality, and noise.

- **Explain the concept of a data-generating process (DGP)** and why forecasting models aim to approximate processes rather than predict exact outcomes.

- **Interpret forecasts as distributions rather than single-point guesses**, and articulate why this perspective is essential for decision-making.
]

---

## Forecasting Impacts Everything and Everyone

.pull-left[
- **Businesses**: Sales forecasts set revenue targets, inventory projections optimize supply chains, and staffing plans ensure workforce readiness during demand fluctuations.

- **Gov.**: Tax revenue and social programs forecasts aid budgeting and resource allocation.

- **Individuals**: Financial forecasts support budgeting, saving, and retirement planning.

- **Weather**: Forecast inform agriculture, disaster prep, and daily decisions.

]

.font80[Source: [Congressional Budget Office](https://www.cbo.gov/publication/61172#_idTextAnchor040)]

<a class="weatherwidget-io" href="https://forecast7.com/en/39d47n84d75/45056/" data-label_1="OXFORD" data-label_2="WEATHER" data-theme="original" >OXFORD WEATHER</a>
<script>
!function(d,s,id){var js,fjs=d.getElementsByTagName(s)[0];if(!d.getElementById(id)){js=d.createElement(s);js.id=id;js.src='https://weatherwidget.io/js/widget.min.js';fjs.parentNode.insertBefore(js,fjs);}}(document,'script','weatherwidget-io-js');
</script>
.font80[Source: [Weather Widget's Forecast](https://weatherwidget.io/)]
</center>

]

---

## Microsoft's Missed Opportunity with Mobile Phones

.font90[
> **Q**: People get passionate when Apple comes out with something new—the iPhone; of course ... **Is that something you'd want them to feel about Microsoft?**

<br>

> **A**: It's sort of a funny question. **Would I trade 96% of the market for 4%?** *(Laughter.)*

> **I want to have products that appeal to everybody.** There's no chance that the iPhone is going to get any significant market share. **No chance.** It's a $500 subsidized item. They may make a lot of money.

> But if you actually take a look at the 1.3 billion phones that get sold, **I'd prefer to have our software in 60% or 70% or 80% of them**, than I would **2% or 3%, which is what Apple might get**.

]
]

.pull-right-2[
.center[
![Steve Ballmer](data:image/png;base64,#../../figures/ceo-ballmerx-large.jpg)

.font90[
Steve Ballmer, Former CEO of Microsoft in his infamous interview with [USA Today 2007](https://web.archive.org/web/20070502033654/https://www.usatoday.com/money/companies/management/2007-04-29-ballmer-ceo-forum-usat_N.htm)
]
]
]

---

## Microsoft's Missed Opportunity: Back of a Napkin Calc.

- Since Q1 2009, **Windows' Mobile OS's market share <= 2.5%**, and is now at 0.02% ([StatCounter](https://gs.statcounter.com/os-market-share/mobile/worldwide/#quarterly-200901-202601)).

- **Apple's Mobile iOS market share > 19%**, and is now at **29.12%** ([StatCounter](https://gs.statcounter.com/os-market-share/mobile/worldwide/#quarterly-200901-202601)).

- Apple's **iPhone revenues** from 2007 to 2025 was **$2.246 trillion** (per [statista](https://www.statista.com/statistics/263402/apples-iphone-revenue-since-3rd-quarter-2007/)).

- Assuming Microsoft could have captured just **5%** of Apple's market revenue `$\rightarrow$` **$112 billion**.

- This estimate **excludes app store and brand value**, which will make the missed opportunity even larger.
]

]

</div>

]

---

## Other Real-World Forecasting Failures in Tech

.pull-left[
  .center[
  
  <img src="data:image/png;base64,#../../figures/1024px-Ibm_px_xt_color.jpg" alt="IBM PC" style="width: auto; height: 190px" />
  
 .font80[**IBM**: Missed the PC revolution.]

]
]

.pull-right[
  .center[
  
  <img src="data:image/png;base64,#../../figures/The_Last_Blockbuster_storefront.jpg" alt="Blockbuster" style="width: auto; height: 190px;" />
  
  .font80[**Blockbuster**: Missed the streaming revolution.]

<img src="data:image/png;base64,#../../figures/Ysearch_2005.png" alt="Yahoo Logo" style="width: auto; height: 190px;" />
 
  .font80[**Yahoo**: Missed the search engine revolution.]
 
]

]

---

## Non-Tech Failures: Red Lobster's Endless Shrimp

.center[
  <img src="data:image/png;base64,#../../figures/red_lobster.png" alt="Red Loster endless shrimp deal was too popular; a key reason for the company's 11 million dollar loss in the third quarter of 2023" style="width: auto; height: 525px;" />
]

---

## Why Do These Stories Matter?

**(1) Forecasting Errors = Real Money Lost**  
  - **Microsoft**: $112 billion in potential mobile phone revenues.
  - **Target:** .bold[Overestimation] leads to unsold stock or overservicing (e.g., [Target's Stock Plunging by 21% due to lower profit and larger inventories](https://www.nytimes.com/2024/11/20/business/target-earnings-holiday-shopping.html?unlocked_article_code=1.sU4.BN7Y.DRvnq7F_52NO&smid=url-share)).
  - **Red Lobster**: $11M in losses due to .bold[underestimating] demand for their endless shrimp deal.

<br>

**(2) Course Relevance:**

This class will teach you how to identify .black[.bold[trends]], .black[.bold[seasonality]], and .black[.bold[cycles]], and .black[.bold[how to apply forecasting tools and models]] so you can **avoid these pitfalls** in your future roles. The goal is to allow you to make **data-driven forecasts**, not just gut-based decisions, and more importantly, be able to **quantify the uncertainty** in your forecasts.

---
class: inverse, center, middle

# Before we formalize forecasting, let’s try it

---

## Can you Avoid Common Forecasting Mistakes?

<countdown-timer class="countdown" id="timer_b7de7aff" minutes="7" seconds="0" update-every="1" tabindex="0" style="top:0;right:0;--countdown-font-size:2em;"></countdown-timer>

- **Scenario**: You are a business analyst at a hotel chain.

- **Problem**: You are tasked with forecasting hotel occupancy for the next 11 months.

- **Data**: You have access to the hotel's monthly room occupancy data from 2023 to 2025. Download the file from the [Week 01: Intro to Forecasting](https://miamioh.instructure.com/courses/250359/modules/924857) module.

- **Task:** .black[.bold[Without the use of any AI tools]], create a forecast for the hotel's occupancy for the next 12 months. The forecast can be made in Excel, R, or Python. .black[.bold[Document the process and the rationale behind your forecasts.]]

- **Non-graded Class Activity:** Briefly, input your logic for the 12-month forecast, and your quantitative forecast for **Janaury 2026** in the next 2 tabs, respectively.

]

Use the editable text-box below to describe your logic for forecasting the hotel's occupancy for the next 12 months. Use bullet points to list your steps.

.can-edit.key-activity1_logic[

**Steps Taken to Generate the Forecasts:** .font70[(Insert below)]

- Edit me  
  
  - ... 
  
  - ...
]

]

- Input your solution for **January 2026** by using the QR code below.

]

]

<button type="button"
        onclick="xrToggle('hotel_logic')"
        aria-controls="hotel_logic"
        aria-expanded="false">
  Let us discuss how to approach such a problem
</button>

.can-edit.key-activity1_viz[

**Fadel's approach to this problem:** .font70[(To be discussed in class)]

- Edit me  
  
  - ... 
  
  - ...
]

]

<details>
  <summary>Let us think of a reasonable solution, which assumes no prior time-series knowledge. </summary>

<small>

```{python 
import pandas as pd

df_hotel = (
  pd.read_csv("../../data/01_hotel_occupancy.csv")
  .assign(date = lambda x: pd.to_datetime(x['date']),
    year = lambda x: x['date'].dt.year  )  )

# plotting of the data hidden for brevity

# compute the average occupancy per year and year-over-year growth rate
yearly_avg = df_hotel.groupby('year')['hotel_occupancy'].mean()
yoy_growth = yearly_avg.pct_change().mean()

monthly_2025 = df_hotel.query("year == 2025") # filter the data for 2025

# forecast the occupancy for 2026
forecast = pd.DataFrame({
    "date": pd.date_range(start="2026-01-01", end="2026-12-01", freq="MS"),
    "forecasted_occupancy": (monthly_2025['hotel_occupancy'] * (1 + yoy_growth) ).round(0).astype(int)
})

forecast.iloc[0:2].reset_index(drop=True)

</small> </details>
```

]
]

---

# Why was this Harder than it Looked?

---

## Good Forecasts Result from a Rigorous Process

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<div class="step-number">1.<br>Problem Definition</div>
    <p>Understand how the forecasts will be used and who requires them.</p>
  </div>

<div class="step-number">2. Gathering Information</div>
    <p>Collect statistical data and the expertise of people involved.</p>
  </div>

<div class="step-number">3. Preliminary Analysis</div>
    <p>Graph the data. Look for trends, seasonality, outliers, and patterns.</p>
  </div>

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    </svg>

<div class="step-number">4. Choosing and Fitting Models</div>
    <p>Select and compare potential models based on the data and problem.</p>
  </div>

<div class="step-number">5. Using and Evaluating the Model</div>
    <p>Generate forecasts and evaluate their accuracy once actual data becomes available.</p>
  </div>

</div>

---

## Before You Touch Data, Ask the Right Questions

### *A deeper look at Step 1: Problem Definition*

**Example scenario:** Forecasting for a manufacturing company.

**Critical questions include:**

- **Granularity:** Do we need forecasts for every single product line, or for groups of products?

- **Aggregation:** Should we forecast for every sales outlet, for outlets grouped by region, or only for total sales?

- **Frequency:** Are we working with weekly, monthly, or annual data?

- **Horizon:**  Are forecasts needed for one month ahead, six months, or ten years?

---

## Choosing the Correct Forecasting Approach

**Key question:**  
Do you have relevant numerical information about the past?

- **No → Qualitative Forecasting**  
  Uses structured, judgment-based approaches when historical data is unavailable or irrelevant  
  (for example, a new product launch).

- **Yes → Quantitative Forecasting**  
  Appropriate when it is reasonable to assume that patterns from the past will persist into the future.

.black[.bold[The Correct Approach Depends on the Context of your Forecasting Problem.]] In this class, we will mainly focus on quantitative forecasting methods.

---

## How Will You Explain the Future?

**Time Series Models**

Uses past values of a variable to forecast its future values by extrapolating trends and seasonal patterns.

.font80[
`$\text{Sales}_{t+1} = f(\text{Sales}_{t}, \ \text{Sales}_{t-1}, \ \text{Sales}_{t-2}, ...)$`
]

![Schematic of a Forecast for Sales](data:image/png;base64,#../../figures/schematic_forecast.png)

]

**Explanatory Models**

Uses other related variables to explain and predict the target variable. Typically, we also include the past values of the target.

.font80[
`$\text{Sales}_{t+1} = f(\text{Sales}_{t}, \ \text{Price}_{t}, \ \text{Advertising}_{t}, \ \text{CompetitorPrice}_{t}, ...)$`
]

![Schematic of an Explanatory Forecast](data:image/png;base64,#../../figures/explanatory_schematic.png)

]

---

## The Heart of Forecasting: Data Observed Over Time

.center[.bold[Our goal is to choose a model that can capture these genuine patterns and project them into the future, while ignoring random fluctuations.]]

---

## The Best Forecast Is Not A number. It's A Distribution.

**Core Idea:** The future is inherently uncertain, so we should think of it as a random variable that can take a range of possible values. The set of these values and their associated probabilities form the **forecast distribution**.

**Key Insight:** The further ahead we try to forecast, the wider the distribution becomes, reflecting the more uncertain we are.

---

## Embracing Uncertainty is the Mark of a Great Forecast[er]

.bold[This is clarity. Not just what we think will happen, but a rigorous explanation of how confident we are in that prediction.]

---

## Reality is Complicated!!

.bold[The principles we have discussed are the tools needed to navigate the complexities of real-world forecasting challenges.]

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<div class="case-title">Case 1</div>
  <div class="case-subtitle">Tableware Manufacturer</div>
  <p>Automating monthly forecasts for hundreds of items with diverse patterns (trends, seasonality, neither).</p>
  </div>

<div class="case-title">Case 2</div>
  <div class="case-subtitle">Pharmaceutical Benefits</div>
  <p>Models must handle trends and seasonality, but also be robust to sudden structural breaks from drug subsidies and competitor entry.</p>
  </div>

<div class="case-title">Case 3</div>
  <div class="case-subtitle">Airline Passenger Traffic</div>
  <p>Accounting for external shocks and irregular events like school holidays, major sporting events, pilot strikes, and competitor actions.</p>
  </div>

</div>

---

## From Chaos to Clarity: You have the Blueprint

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<div class="journey-step chaos-box">
    <div class="journey-title">We started in Chaos…</div>
    <div class="journey-text">
      …with a history of high-stakes guesswork and
      famous failed predictions.
    </div>
  </div>

<div class="journey-step clarity-box">
    <div class="journey-title">We found a Path to Clarity…</div>
    <div class="journey-text">
      …by defining the problem, understanding predictability,
      and following a rigorous 5-step process.
    </div>
  </div>

<div class="journey-step insight-box">
    <div class="journey-title">The Destination is Insight.</div>
    <div class="journey-text">
      …moving beyond single numbers to think in forecast
      distributions and embrace uncertainty.
    </div>
  </div>

</div>

<div class="footer-text">
  You now have the foundational framework.<br>
  You’re ready to build the models.
</div>

<br>

**So, with this conceptual understanding, let us get moving.**

---
class: inverse, center, middle

# What Kind of Data are we Forecasting With? <br><br>(Types of Data Over Time and the Components of a Time Series)

---

## Cross-Sectional Data

**Cross-sectional data** captures multiple variables at a single point in time for each
observation; e.g., .bold[all the variables within a given observation] in the [DoL's LCA Disclosure Data for 2025 Q4](https://www.dol.gov/sites/dolgov/files/ETA/oflc/pdfs/LCA_Disclosure_Data_FY2025_Q4.xlsx) were collected simultaneously.

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JC50 - Software Quality Assurance Analysts and Testers","Hematology Oncology Physician","SOFTWARE ENGINEER","Java Full Stack Developer","SOFTWARE ENGINEER","Software Development Manager","Film Director","ENT Fellow (Rhinology)","SALES ACCOUNT MANAGER","Vice President, Lead Software Engineer","Analyst - Testing","Test Engineer I","Software Developer","Java Developer - Applications","Senior Marketing Campaign Analyst","Quality Engineer","Research and Development Manager","OEM Senior Sales Engineer - Americas, Membrane Solutions","Associate Manager Software Engineering","JAVA ENGINEER","QA Automation Test Engineer","Architect","Development Manager Senior","Power BI Developer","Post Doctoral Scholar","MATHEMATICS TEACHER","Technical Application Engineer","Developer","Architect","MARKET RESEARCH ANALYST","IT Architect","Assistant Director, Career and Employer Engagement","SAP Consultant","SOFTWARE DEVELOPER","IT Consultant (SAP)","Project Delivery Specialist","Cardiologist","Pavement Research Engineer","Developer","Software Developer","SOFTWARE DEVELOPER","Software Engineer - Sr. Consultant level","SOFTWARE DEVELOPER","Guidewire Developer","HIL Test Engineer","Architect","System Administrator","WORKDAY HCM CONSULTANT","INFORMATICA AND HADOOP DEVELOPER","User Interface Designer","Program Manager -ProdDev","Tech Architecture Assoc Manager","Software Developer","Workday Developer","Business Intelligence Analyst","HIL Test Engineer","Hospitalist Physician-Internal Medicine","Senior Software Engineer","Quality Engineer","Architect","Test Engineer","Software Consultant","Sr. Oracle Business Analyst","Information Technology Project Manager","Developer","Sr Mgr JC45-Software Quality Assurance Analysts and Testers","Assistant Director Human Performance Coach -Goggin","Industrial Engineer","SOFTWARE ENGINEER","Software Engineer","Data Scientist Manager","Senior Software Engineer","Structural Heart Fellow","Business Analyst","Manager, Data & Analytics Management","ORACLE HCM CONSULTANT","DESIGN SPECIALIST","Computer Programmer","OB/GYN Physician","Oracle Cloud Architect","Business Intelligence Developer","Customer Success Engineer","SOFTWARE DEVELOPER","graduate physician trainee","Software Developer","Product Development Engineer","Service Engineer","hospital medicine physician","cardiologist","SAP Functional Analyst - Level 3 - OTC","graduate physician trainee","pulmonary/critical care physician","PLM Developer","Computer Programmer","Developer","Software Develpoment Manager","Engineer I","Data Engineer","Staff Chaplain","Senior Test Engineer","SOFTWARE DEVELOPER","Business Analyst","Business Analyst","Information Technology Project Manager","Information Technology Project Manager","Process Development Engineer","Architect","Nephrologist","Software Developer","Computer Programmer","QA Analyst","QA Engineer","Data Engineer","Data Engineer","Systems Analyst and Tech-Stack Coordinator","Industrial Engineer","Openshift Engineer","Developer","Associate Staff, Urologist","Architect","Software Developer","Sr. Engineer","Post Doctoral Scholar","Senior SAP BI Analyst","Analyst - Information Security","Software Developer","Vice President, Sr Manager of Software Engineering","Pricing Data Scientist","Applications Consultant 3","User Interface Designer","Sr. Engineer","Sr. Software Engineer","Research & Development Analyst","Director of Treasury","Research Assistant Professor","Assistant Professor","Computer Systems Analyst","Research Scientist","Sr. Engineer","NPDI Procurement Lead","Revenue Cycle Manager","Math Teacher","Director - Senior Solutions Architect","Developer","Director - Product Development","Staff, Cardiothoracic Anesthesiology","Internal Medicine Physician","Project Manager","Sr. Engineer","Sr. Data Engineer","Assistant Professor - Clinical","PRODUCIBILITY ENGINEER II","Design Engineer","Medical Resident","Assistant Manager","Data Scientist II","User Interface Designer","Software Engineer","Data Engineer","Network Engineer","Researcher 1","Manager IT","Technical Lead","Research Scientist","Senior Data Engineer","Senior Quality Engineer","Researcher 1","Software Engineer Senior","Software Developer","Systems Analyst","HCM / HRIS Analyst / Consultant","Java Developer","Assistant Professor","Software Engineer","Software Engineer","Advanced Data Engineer","Design Engineer","Site Reliability Engineer","Visiting Assistant Professor","ESL TEACHER","Sr. Engineer","pathologist","Associate Professor of Religion and Philosophy","User Interface Designer","Software Engineer","User Interface Designer","Software Programmer II","Assistant Professor"],["The Ohio State University","The Ohio State University","OCLC, Inc.","Summa Physicians, Inc.","The Ohio State University","Technodrive Business Solutions, Inc.","shark&minnow inc.","Summa Physicians, Inc.","ND Paper Inc.","Cleveland Clinic","Columbus Technology Solutions, Inc.","Universal Insurance Managers, Inc.","COGNIZANT TECHNOLOGY SOLUTIONS US CORP","Lakshya Technologies, Inc.","Cleveland Clinic","Acuity Brands Lighting, Inc.","Upward Innovations LLC","COGNIZANT TECHNOLOGY SOLUTIONS US CORP","OhioHealth Physician Group, Inc.","RACEDOG LIMITED","ITvorks Inc","RACEDOG LIMITED","London Computer Systems, Inc.","TRG Studios Inc.","Western Reserve Health Education, Inc.","Mexichem Specialty Resins, Inc.","JPMorgan Chase & Co.","Tata Consultancy Services Limited","Transportation Research Center, Inc.","Ciberlynx Inc","BIZINTEX, INC","NaviStone, Inc.","Columbus Technology Solutions, Inc.","Locus Holdings LLC","Air Products and Chemicals, Inc.","Computer Sciences Corporation","E-GIANTS TECHNOLOGIES LLC","Technumen, Inc.","Tata Consultancy Services Limited","Worldpay, LLC","ETECH GLOBAL IT SOLUTIONS LLC","The Ohio State University","HORIZON EDUCATIONAL SERVICES OF COLUMBUS INC","MRS Electronic, Inc.","Tata Consultancy Services Limited","Tata Consultancy Services Limited","3AMIGOSIT LLC","Midwest Motor Supply Co.","The Ohio University","Prime S4 Technologies LLC","TANA SYSTEMS INC","Propel Solutions, Inc.","Deloitte Consulting LLP","ProMedica Northwest Ohio Cardiology Consultants","RAP Management, LLC","TATA CONSULTANCY SERVICES LIMITED","Vertex Computer Systems, Inc.","AG INFOTEK INC.","Visa U.S.A. Inc.","TANA SYSTEMS INC","Technumen, Inc.","L&T Technology Services Limited","Tata Consultancy Services Limited","Tata Consultancy Services Limited","QUANTUM TECHNOLOGIES LLC","GMA SOFT INC.","Tata Consultancy Services Limited","Oracle America, Inc.","Accenture LLP","SMACT Works, Inc.","Technumen, Inc.","BDG Wrap-Tite, Inc.","L&T Technology Services Limited","Ohio Valley Physicians, Inc.","The Kroger Company","Wailea Systems LLC","TATA CONSULTANCY SERVICES LIMITED","L&T Technology Services Limited","Hadiamondstar Software Solutions LLC","Clopay Corporation","LTIMindtree Limited","Tata Consultancy Services Limited","COGNIZANT TECHNOLOGY SOLUTIONS US CORP","Miami University","Alten Technology USA, Inc.","META SOFT INC","COGNIT AI INC","Precision eControl, LLC","The Kroger Company","The Christ Hospital Physicians LLC","Technology Hub Inc","Cardinal Health","QUANTUM TECHNOLOGIES LLC","CRYSTAL PROJECT, INC.","Tribco Inc.","OhioHealth Physician Group, Inc.","Arche Resources LLC","Shark Analytics LLC","QlikTech Inc.","KSOFT SYSTEMS INC","Cleveland Clinic Foundation","Tagma Solutions, Inc.","ANGSTROM FIBER SIDNEY","Bright Machines, Inc.","Cleveland Clinic Foundation","Cleveland Clinic Foundation","Cintas Corporation","Cleveland Clinic Foundation","Cleveland Clinic Foundation","Ams Tec Solutions LLC","DATAMART SYSTEMS, INC.","Tata Consultancy Services Limited","Winsupply Inc","Jones & Henry Engineers, Ltd.","Exact Benefits Group LLC.","OhioHealth Corp.","OCLC, Inc.","KSOFT SYSTEMS INC","Technology Hub Inc","Aries Computer Systems, Inc.","LTIMindtree Limited","LTIMindtree Limited","TRI-TECH LABORATORIES, LLC","Tata Consultancy Services Limited","Premier Renal Care Associates, LLC","SIPTEK GROUP INC","Tribco Inc.","TECHQUEST SOLUTIONS, LLC.","Horizon IT Inc","American Analyst, Inc.","TECHQUEST SOLUTIONS, LLC.","Mytee LLC","B D G WRAP-TITE, INC.","Lambdanets Inc","TATA CONSULTANCY SERVICES LIMITED","Cleveland Clinic","Tata Consultancy Services Limited","V-Soft Consulting Group, INC","MSAII LLC","The Ohio State University","Great Lakes Cheese Co. Inc.","Tata Consultancy Services Limited","DATAMETRICS SOFTWARE SYSTEMS, INC","JPMorgan Chase & Co.","Mettler-Toledo, LLC","Capgemini America Inc","Tata Consultancy Services Limited","MSAII LLC","SYSTEM SOFT TECHNOLOGIES, LLC","Progressive Casualty Insurance Company","CommuteAir LLC","The Ohio State University","The Ohio State University","Quadrant Technologies LLC","The Ohio State University","MSAII LLC","Vertiv Corporation","Wellness Card LLC","La Salle High School","Exel, Inc.","Tata Consultancy Services Limited","Luxottica of America Inc.","Cleveland Clinic","Highland Health Providers Corp.","MSAII LLC","MSAII LLC","Caprus IT Inc","The Ohio State University","Intelligrated Systems, Inc.","MSAII LLC","Dayton Osteopathic Hospital","Genpact LLC","Truist Bank","Tata Consultancy Services Limited","WORK FOR PRO INC.","Navvis & Company, LLC","Kenyon College","The Ohio State University","HM Health Solutions, Inc.","Tata Consultancy Services Limited","Cleveland Clinic Foundation","The Kroger Company","The Kroger Company","The Ohio State University","United Services Automobile Association","DATAMETRICS SOFTWARE SYSTEMS, INC","COMPUNNEL SOFTWARE GROUP, INC","ERP Analysts, Inc.","Congensys Corp.","The Ohio State University","VISTALTECH INC","U.S. Bank National Association","The Kroger Company","MSAII LLC","Emplifi Inc.","The Ohio State University","HORIZON EDUCATIONAL SERVICES OF COLUMBUS INC","MSAII LLC","Cleveland Clinic Foundation","Muskingum University","TATA CONSULTANCY SERVICES LIMITED","MSAII LLC","Tata Consultancy Services Limited","Mphasis Corporation","The Ohio State University"],["OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH","OH"],[98004,63100,123000,211273,72000,82514,44000,211273,79950,490000,103000,103700,119954,95139,185585.95,102627,76000,86507,495000,86000,73000,86000,162493,59000,88179.23,150700,137400,136125,85000,75500,95742,75619,75000,99001.75999999999,151300,111010,102627,83243,137600,167000,95139,61008,51700,70387,137600,137600,55000,130000,62022,102630,73000,70000,83242,630000,78280,161000,86500,77438,203800,73000,120001,93000,136125,136125,62483,107619,136125,180305.6,223800,85000,115001,62500,93000,315000,126357.28,85900,102950,93242,93226,141398.66,161907,136125,100235,76000,107000,90000,89419,155000,136979.7,239200,65147,175000,62483,81250,52499,331000.02,102000,102700,230000,73000,77137,95000,74000.00999999999,120000,280500,620000,130541,82826,355000,77438,70000,102200,150000,75545,62506.19,76939.2,115803.57,73000,65147,103418,126204,132628,92000,137600,260000,102627,52499,72000,67683,78400,74000,85000,140000,90000,137600,490000,136125,103000,90000,61008,158700,137590,95139,172000,114288.92,126618,102200,90000,125000,90300,113855,105000,348741,90000,72862,90000,120000,60000,75200,156743.66,102200,173184,550000,230000,121000,90000,105997,134247,92846,90000,62960,84090,130490,102950,103000,132241.95,94391,56800,113568,137600,115500,142773.5,124906.81,58488,166950,95139,95000,103210,103000,386112,102627,115500,141384.93,90000,96600,67800,64820,90000,340000,55980,102200,85000,102200,126750,94000]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th>Date<\/th>\n      <th>Job Title<\/th>\n      <th>Employer<\/th>\n      <th>WORKSITE_STATE<\/th>\n      <th>Salary<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"pageLength":7,"columnDefs":[{"targets":4,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatCurrency(data, \"$\", 0, 3, \",\", \".\", true, null);\n  }"},{"className":"dt-right","targets":4},{"name":"Date","targets":0},{"name":"Job Title","targets":1},{"name":"Employer","targets":2},{"name":"WORKSITE_STATE","targets":3},{"name":"Salary","targets":4}],"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[7,10,25,50,100]}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

]

---

## Time Series Data

**Time series data** captures a single variable at multiple points in time; e.g., the [daily stock prices for Apple](https://finance.yahoo.com/quote/AAPL/history?p=AAPL) or our **simulated monthly hotel room occupancy** dataset.

---

## Panel Data

**Panel data** captures multiple variables at multiple points in time for each observation; e.g., the [Panel Study of Income Dynamics](https://psidonline.isr.umich.edu/) or the [World Bank's World Development Indicators](https://databank.worldbank.org/source/world-development-indicators).

.font80[
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]

**Source:** Data queried from the [World Bank Data](https://datacatalog.worldbank.org/) using the [wbstats](https://cran.r-project.org/web/packages/wbstats/wbstats.pdf) <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:gold;overflow:visible;position:relative;"><path d="M50.7 58.5L0 160H208V32H93.7C75.5 32 58.9 42.3 50.7 58.5zM240 160H448L397.3 58.5C389.1 42.3 372.5 32 354.3 32H240V160zm208 32H0V416c0 35.3 28.7 64 64 64H384c35.3 0 64-28.7 64-64V192z"/></svg> in R. The printed results show a snapshot of 7 variables (out of a much larger panel dataset). You can think of panel data as a cross-sectional dataset with a longitudinal/time component.
]

---

## Components of Time Series Data: Trend

- **Trend**: A long-term increasing or decreasing pattern over time.

- **Example**: The [US GDP](https://fred.stlouisfed.org/series/GDP) has a long-term upward trend.

---

## Components of Time Series Data: Seasonality

**Seasonality** refers to the property of a time series that displays REGULAR patterns that repeat at a constant frequency (*m*). For example, the [number of retail trade workers](https://fred.stlouisfed.org/series/CEU4200000001) has a seasonal pattern (with an upward trend).

---

## Components of Time Series Data: Multiple Seasonality

**Multiple seasonality** refers to the property of a time series that displays multiple seasonal patterns that repeat at different frequencies.

---

## Components of Time Series Data: Cycles

**Cycles** refer to the property of a time series that displays irregular patterns that repeat at irregular frequencies. For example, the [US Total Vehicle Sales](https://fred.stlouisfed.org/series/TOTALSA) has business cycles that are influenced by economic conditions and advancements in vehicle technologies.

---

## Components of Time Series Data: Cycles

---

# Kahoot Competition #01

To assess your understanding and retention of the topics covered so far, you will **compete in a Kahoot competition (consisting of 5 questions)**:

- Go to <https://kahoot.it/>

- Enter the game pin, which will be shown during class

- Provide your first (preferred) and last name

- Answer each question within the allocated 20-second window (**fast and correct answers provide more points**)

<br>

**Winning the competition involves having as many correct answers as possible AND taking the shortest duration to answer these questions.** The winner <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:gold;overflow:visible;position:relative;"><path d="M400 0H176c-26.5 0-48.1 21.8-47.1 48.2c.2 5.3 .4 10.6 .7 15.8H24C10.7 64 0 74.7 0 88c0 92.6 33.5 157 78.5 200.7c44.3 43.1 98.3 64.8 138.1 75.8c23.4 6.5 39.4 26 39.4 45.6c0 20.9-17 37.9-37.9 37.9H192c-17.7 0-32 14.3-32 32s14.3 32 32 32H384c17.7 0 32-14.3 32-32s-14.3-32-32-32H357.9C337 448 320 431 320 410.1c0-19.6 15.9-39.2 39.4-45.6c39.9-11 93.9-32.7 138.2-75.8C542.5 245 576 180.6 576 88c0-13.3-10.7-24-24-24H446.4c.3-5.2 .5-10.4 .7-15.8C448.1 21.8 426.5 0 400 0zM48.9 112h84.4c9.1 90.1 29.2 150.3 51.9 190.6c-24.9-11-50.8-26.5-73.2-48.3c-32-31.1-58-76-63-142.3zM464.1 254.3c-22.4 21.8-48.3 37.3-73.2 48.3c22.7-40.3 42.8-100.5 51.9-190.6h84.4c-5.1 66.3-31.1 111.2-63 142.3z"/></svg> of the competition will receive a **0.15 bonus on Assignment 01**. Good luck!!!

**P.S:** The Kahoot competition will have **no impact on your grade**. It is a **fun** way of assessing your knowledge, motivating you to ask questions about topics covered that you do not have a full understanding of it, and providing me with some data that I can use to pace today's class. 
]

---

# The Data Generating Process

---

## The Idea of a Data Generating Process (DGP)

- A **time series** is defined as a **sequence of observations** recorded at regular time intervals.

- Any time series is generated by some kind of mechanism, which is often referred to as a **data generating process (GDP)**. For example, the hotel occupancy dataset is impacted by:   
  - .black[.bold[season]], .black[.bold[holidays]], .black[.bold[economic conditions]], and .black[.bold[marketing campaigns]];  
  - .black[.bold[number of rooms]], .black[.bold[room rates]], and .black[.bold[customer satisfaction]];   
  - .black[.bold[weather]], .black[.bold[local events]], and .black[.bold[competition]]; and 
  - .black[.bold[number of rooms already booked]], .black[.bold[room cancellations]], and .black[.bold[no-shows]].

- The **DGP** is the **underlying theoretical mechanism** that generates the data we observe.  
   - Accounts for both systematic patterns (e.g., trend, seasonality) and randomness.    
- **But**: In real-world settings, there is often **no perfectly known** DGP.    
  - Any formula or model we write is an approximation of the **unknowable “truth.”**

---

## Model vs. Reality — The Map Analogy for DGPs

.pull-left[
- **A map ≠ the territory**:  
  - We use maps to navigate, but they are always simplified.  
  - Similarly, a forecast model ≠ reality—it is a *purposeful* simplification.

- **Different maps for different needs**:  
  - A tourist map highlights landmarks, while a transportation map focuses on roads to inform navigation.  
  - Each addresses *specific* questions, just as we build different forecasting models for different objectives.
]

<br>

![](data:image/png;base64,#../../figures/transportation_oxford.png)
]

---

## Why Use DGPs If They Do not Actually Exist?

**(1) Guiding Principle:**    
   - Thinking in terms of a *hypothetical* DGP helps us design or select reasonable model structures.  
   - E.g., we incorporate domain insights: “Does our hotel occupancy data show strong seasonality?”

**(2) Clarifying Assumptions:**    
   - Even if the DGP is not known, stating assumptions (e.g., no trend, constant variance) makes our models testable and improvable.

**(3) Iterative Refinement:**    
   - As new data contradict our assumptions, we adjust our “map” of reality.  
   - In forecasting, we continually update models to capture changing conditions.

---

## Key DGP Takeaways

- **All Models Are Wrong…**  
  - ...but some are *useful* for forecasting, planning, or decision-making.

- **The DGP Is a Useful Fiction**  
  - We talk about it to structure our thinking.  
  - We never truly “see” it; we only see **data**.

- **Practical Implication**  
  - A good model is *close enough* to guide accurate forecasts.  
  - Remain aware of model limitations and be ready to adapt.

---

# "What Can (and Can not) We Forecast?"

---

## Rank these Scenarios in Terms of Forecastability

<countdown-timer class="countdown" id="timer_5b4e1037" minutes="2" seconds="0" update-every="1" tabindex="0" style="top:0;right:0;--countdown-font-size:2em;"></countdown-timer>

- **Rank** each scenario (in the next tab) from **easiest** (1) to **hardest** (6) to predict.

- **Submit** your ranking by clicking [here](https://www.menti.com/al4qbc8hg3jn)

]

- <svg aria-hidden="true" role="img" viewBox="0 0 576 512" style="height:1em;width:1.12em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#2ecc71;overflow:visible;position:relative;"><path d="M0 112.5V422.3c0 18 10.1 35 27 41.3c87 32.5 174 10.3 261-11.9c79.8-20.3 159.6-40.7 239.3-18.9c23 6.3 48.7-9.5 48.7-33.4V89.7c0-18-10.1-35-27-41.3C462 15.9 375 38.1 288 60.3C208.2 80.6 128.4 100.9 48.7 79.1C25.6 72.8 0 88.6 0 112.5zM288 352c-44.2 0-80-43-80-96s35.8-96 80-96s80 43 80 96s-35.8 96-80 96zM64 352c35.3 0 64 28.7 64 64H64V352zm64-208c0 35.3-28.7 64-64 64V144h64zM512 304v64H448c0-35.3 28.7-64 64-64zM448 96h64v64c-35.3 0-64-28.7-64-64z"/></svg> **Lottery winning numbers for next weekend**

- <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#f1c40f;overflow:visible;position:relative;"><path d="M375.7 19.7c-1.5-8-6.9-14.7-14.4-17.8s-16.1-2.2-22.8 2.4L256 61.1 173.5 4.2c-6.7-4.6-15.3-5.5-22.8-2.4s-12.9 9.8-14.4 17.8l-18.1 98.5L19.7 136.3c-8 1.5-14.7 6.9-17.8 14.4s-2.2 16.1 2.4 22.8L61.1 256 4.2 338.5c-4.6 6.7-5.5 15.3-2.4 22.8s9.8 13 17.8 14.4l98.5 18.1 18.1 98.5c1.5 8 6.9 14.7 14.4 17.8s16.1 2.2 22.8-2.4L256 450.9l82.5 56.9c6.7 4.6 15.3 5.5 22.8 2.4s12.9-9.8 14.4-17.8l18.1-98.5 98.5-18.1c8-1.5 14.7-6.9 17.8-14.4s2.2-16.1-2.4-22.8L450.9 256l56.9-82.5c4.6-6.7 5.5-15.3 2.4-22.8s-9.8-12.9-17.8-14.4l-98.5-18.1L375.7 19.7zM269.6 110l65.6-45.2 14.4 78.3c1.8 9.8 9.5 17.5 19.3 19.3l78.3 14.4L402 242.4c-5.7 8.2-5.7 19 0 27.2l45.2 65.6-78.3 14.4c-9.8 1.8-17.5 9.5-19.3 19.3l-14.4 78.3L269.6 402c-8.2-5.7-19-5.7-27.2 0l-65.6 45.2-14.4-78.3c-1.8-9.8-9.5-17.5-19.3-19.3L64.8 335.2 110 269.6c5.7-8.2 5.7-19 0-27.2L64.8 176.8l78.3-14.4c9.8-1.8 17.5-9.5 19.3-19.3l14.4-78.3L242.4 110c8.2 5.7 19 5.7 27.2 0zM256 368a112 112 0 1 0 0-224 112 112 0 1 0 0 224zM192 256a64 64 0 1 1 128 0 64 64 0 1 1 -128 0z"/></svg> **Sunrise time in Oxford, Ohio on January 1, 2026**

- <svg aria-hidden="true" role="img" viewBox="0 0 320 512" style="height:1em;width:0.62em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#e74c3c;overflow:visible;position:relative;"><path d="M160 64c-26.5 0-48 21.5-48 48V276.5c0 17.3-7.1 31.9-15.3 42.5C86.2 332.6 80 349.5 80 368c0 44.2 35.8 80 80 80s80-35.8 80-80c0-18.5-6.2-35.4-16.7-48.9c-8.2-10.6-15.3-25.2-15.3-42.5V112c0-26.5-21.5-48-48-48zM48 112C48 50.2 98.1 0 160 0s112 50.1 112 112V276.5c0 .1 .1 .3 .2 .6c.2 .6 .8 1.6 1.7 2.8c18.9 24.4 30.1 55 30.1 88.1c0 79.5-64.5 144-144 144S16 447.5 16 368c0-33.2 11.2-63.8 30.1-88.1c.9-1.2 1.5-2.2 1.7-2.8c.1-.3 .2-.5 .2-.6V112zM208 368c0 26.5-21.5 48-48 48s-48-21.5-48-48c0-20.9 13.4-38.7 32-45.3V208c0-8.8 7.2-16 16-16s16 7.2 16 16V322.7c18.6 6.6 32 24.4 32 45.3z"/></svg> **Maximum temperature in Oxford, Ohio tomorrow**

- <svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:#9b59b6;overflow:visible;position:relative;"><path d="M349.4 44.6c5.9-13.7 1.5-29.7-10.6-38.5s-28.6-8-39.9 1.8l-256 224c-10 8.8-13.6 22.9-8.9 35.3S50.7 288 64 288H175.5L98.6 467.4c-5.9 13.7-1.5 29.7 10.6 38.5s28.6 8 39.9-1.8l256-224c10-8.8 13.6-22.9 8.9-35.3s-16.6-20.7-30-20.7H272.5L349.4 44.6z"/></svg> **Daily electricity demand in 3 days**

]

]

---

## Relating It Back to the DGP

- **Different Types of DGPs**  
  1. **Deterministic (or nearly so)**: Sunset times, tidal schedules.  
  2. **Complex & Partly Stochastic**: Weather, financial markets.  
  3. **Pure Randomness**: Lottery draws.

- **Key Lesson**  
  - *All* these processes have a DGP—some are more “knowable” than others.  
  - *Forecastability* depends on how much of that DGP is deterministic vs. random and how well we can model it.

---

# Recap

---

## Summary of Main Points

By now, you should be able to do the following:

.font90[
- **Explain why forecasting is both valuable and difficult**, using real-world business and policy examples.

- **Recognize the fundamental limits of forecasting**, including uncertainty, randomness, and the difference between prediction and explanation.

- **Distinguish forecasting problems from other analytics tasks**, such as regression and classification, and explain why time ordering matters.

- **Identify what types of phenomena are forecastable and which are not**, based on the presence or absence of systematic structure.

- **Describe the core components of a time series**, including trend, seasonality, and noise.

- **Explain the concept of a data-generating process (DGP)** and why forecasting models aim to approximate processes rather than predict exact outcomes.

- **Interpret forecasts as distributions rather than single-point guesses**, and articulate why this perspective is essential for decision-making.
]

---

## 📝 Review and Clarification 📝

1. **Class Notes**: Take some time to revisit your class notes for key concepts.

2. **Zoom Recording**: Recording will be made available on Canvas ~ 3-4 hours after class.

3. **Reference Textbook**: [Chapter 01 of FPPPy](https://otexts.com/fpppy/nbs/01-intro.html) provides a comprehensive overview of the topics covered today.

3. **Review AI Recaps:** Generated from the reference chapter and are meant to reinforce most of the same core ideas.

4. **Questions**: Do not pile up. Ask in real-time, email or come to office hours.

]

**📺 Slide Deck Video (click to play)**
<iframe width="100%" height="230"
src="https://www.youtube.com/embed/lfPB8lH7UcE?si=uVeIfJhXq5idJqAi"
title="NotebookLM Slide Deck Review"
frameborder="0"
allow="accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture"
allowfullscreen>
</iframe>

<br>

**🎧 Slide Deck Podcast (click to play)**
<iframe src="https://drive.google.com/file/d/1bASIDZyUQBPa2uZDwB-fWqQJ0-qnQxgu/preview"
width="100%" height="70"
allow="clipboard-write">
</iframe>

]

---

## 📖 Recommended Readings: 🐍 Python Prep 📖

#### 🐍 Optional Python Prep

- [Data Structures](https://docs.python.org/3/tutorial/datastructures.html)

---

## 📖 Recommended Reading: LLM Prep 📖

.pull-left[
.font90[
#### 🤖 LLM Prep (Scan for main concepts)
- [A Very Gentle Introduction to Large Language Models without the Hype](https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5f67941fa59e)
]
]

.pull-right[
.font90[
**📺 Optional Video (LLM Prep)**  
<iframe width="100%" height="260"
src="https://www.youtube.com/embed/F5Gs6-C0DiA?autoplay=0"
title="LLM Prep Review Video"
frameborder="0"
allow="accelerometer; clipboard-write; encrypted-media; gyroscope; picture-in-picture"
allowfullscreen>
</iframe>
]
]

---

## 🎯 Assignment 🎯

- Complete [Assignment 01](https://miamioh.instructure.com/courses/250359/quizzes/776091) on Canvas to reinforce your understanding of today's class.

<div style="background: #fefce8; border-left: 4px solid #facc15; padding: 18px 22px; margin-bottom: 25px; border-radius: 0 8px 8px 0;"><strong>Before You Begin:</strong><p style="margin: 10px 0 0 0; font-size: 14px; color: #451a03;">This assignment has two parts. Make sure you have reviewed the materials below.</p><ul style="margin: 12px 0 0 0; padding-left: 20px; font-size: 14px; color: #451a03;"><li><strong style="color: #000;">Recommended review for Class 01:</strong><ul style="margin: 8px 0 0 0; padding-left: 20px;"><li><strong style="color: #000;">Slide deck</strong></li><li><strong style="color: #000;">Reference Textbook:</strong> <a style="color: #2563eb; text-decoration: underline;" href="https://otexts.com/fpppy/nbs/01-intro.html" target="_blank" rel="noopener">Chapter 01 of FPPPy</a> provides a comprehensive overview of the topics covered today.</li><li><strong style="color: #000;">Zoom recording</strong></li></ul></li><li style="margin-top: 12px;"><strong style="color: #000;">NotebookLM GenAI Summaries</strong> <span style="font-size: 13px; color: #451a03;">(optional, but a different way to engage with the material)</span>:<ul style="margin: 8px 0 0 0; padding-left: 20px;"><li><a style="color: #2563eb; text-decoration: underline;" href="https://youtu.be/lfPB8lH7UcE" target="_blank" rel="noopener">01_BI__Data_to_Decisions.mp4</a> <span style="font-size: 13px; color: #451a03;">(7-minute video highlight)</span></li><li><a style="color: #2563eb; text-decoration: underline;" href="https://drive.google.com/open?id=1bASIDZyUQBPa2uZDwB-fWqQJ0-qnQxgu&usp=drive_fs" target="_blank" rel="noopener">01_From_Sheep_Liver_to_Forecasting_Algorithms.m4a</a> <span style="font-size: 13px; color: #451a03;">(~15-minute explanation in a podcast fashion; you may want to download first)</span></li></ul></li><li style="margin-top: 14px;"><strong style="color: #000;">Recommended Warmup for Class 02:</strong><ul style="margin: 8px 0 0 0; padding-left: 20px;"><li><strong>Python Data Structures:</strong> <a style="color: #2563eb; text-decoration: underline;" href="https://docs.python.org/3/tutorial/datastructures.html" target="_blank" rel="noopener">https://docs.python.org/3/tutorial/datastructures.html</a> <span style="font-size: 13px; color: #451a03;">(a bit dry, but I recommend scanning it)</span></li><li><strong>LLM Usage Prep:</strong><ul style="margin: 8px 0 0 0; padding-left: 20px;"><li>Scanning the <a style="color: #2563eb; text-decoration: underline;" href="https://mark-riedl.medium.com/a-very-gentle-introduction-to-large-language-models-without-the-hype-5f67941fa59e" target="_blank" rel="noopener">A Very Gentle Introduction to Large Language Models without the Hype</a> Medium article</li><li>Watching its <strong>10-minute</strong> NotebookLM GenAI Video Summary that I created based on it: <a style="color: #2563eb; text-decoration: underline;" href="https://youtu.be/F5Gs6-C0DiA" target="_blank" rel="noopener">https://youtu.be/F5Gs6-C0DiA</a></li></ul></li></ul></li></ul></div>